Workflow for integrating mesoscale heterogeneities in materials structure with process simulation of titanium alloys

  • Ayman A SalemEmail author
  • Joshua B Shaffer
  • Daniel P Satko
  • S Lee Semiatin
  • Surya R Kalidindi


In this paper, a generalized workflow is outlined for the necessary integration of multimodal measurements and multiphysics models at multiple hierarchical length scales demanded by an Integrated Computational Materials Engineering (ICME) approach to accelerated materials development. Recognizing that multiple choices or techniques are typically available in each of the main steps, several exemplary analyses are detailed utilizing mainly the alpha/beta titanium alloys as an illustrative case. It is anticipated that the use and further refinement of these workflows will promote transparency and engender intimate collaborations between materials experts and manufacturing/design specialists by providing an understanding of the various mesoscale heterogeneities that develop naturally in the workpiece as a direct consequence of the inherent heterogeneity imposed by the manufacturing history (i.e., different thermomechanical histories at different locations in the sample). More specifically, this article focuses on three main areas: (i) data science protocols for efficient analysis of large microstructure datasets (e.g., cluster analysis), (ii) protocols for extracting reduced descriptions of salient microstructure features for insertion into simulations (e.g., regions of homogeneity), and (iii) protocols for direct and efficient linking of materials models/databases into process/performance simulation codes (e.g., crystal plasticity finite element method).


ICME Microstructure informatics Higher-order statistics Materials big data Macrozones Region of homogeneity Representative orientation distribution Alpha/beta titanium alloys 



Support from the Air Force Research Laboratory and Air Force Office of Scientific Research is gratefully acknowledged. In particular, AAS, JBS, and DPS were partially supported by contract no. FA865009D5600 (Dr. J. Calcaterra, program manager). SRK was supported by the Air Force Office of Scientific Research, MURI contract no. FA9550-12-1-0458.

Supplementary material

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  1. 1.
    Semiatin SL, Glavicic MG, Shevchenko SV, Ivasishin OM, Chun YB, Hwang SK: Modeling and simulation of texture evolution during the thermomechanical processing of titanium alloys. In ASM Handbook, Vol 22A: fundamentals of modeling for metals processing. Edited by: Semiatin SL, Furrer DU. ASM International, Materials Park; 2009:536–552.Google Scholar
  2. 2.
    Semiatin SL, Furrer DU: Modeling of microstructure evolution during the thermomechanical processing of titanium alloys. In ASM Handbook, Volume 22A: fundamentals of modeling for metals processing. Edited by: Semiatin SL, Furrer DU. ASM International, Materials Park; 2009:522–535.Google Scholar
  3. 3.
    Agrawal A, Deshpande PD, Cecen A, Basavarsu GP, Choudhary AN, Kalidindi SK: Exploration of data science techniques to predict fatigue strength of steel from composition and processing parameters. Integr Mater Manuf Innov 2014, 3: 8. 10.1186/2193-9772-3-8Google Scholar
  4. 4.
    Gibbs JW, Voorhees P: Segmentation of four-dimensional, X-ray computed tomography data. Integr Mater Manuf Innov 2014, 3: 6. 10.1186/2193-9772-3-6Google Scholar
  5. 5.
    Lütjering G, Williams JC: Titanium. Springer, New York; 2007.Google Scholar
  6. 6.
    Salem A, Glavicic M, Semiatin S: A coupled EBSD/EDS method to determine the primary-and secondary-alpha textures in titanium alloys with duplex microstructures. Mater Sci Eng A 2008, 494(1):350–359. 10.1016/j.msea.2008.06.022Google Scholar
  7. 7.
    Kaufman L, Rousseeuw PJ: Finding groups in data: an introduction to cluster analysis. John Wiley & Sons, Hoboken, NJ, USA; 2009.Google Scholar
  8. 8.
    Kalidindi SR, Niezgoda SR, Salem AA: Microstructure informatics using higher-order statistics and efficient data-mining protocols. JOM 2011, 63(4):34–41. 10.1007/s11837-011-0057-7Google Scholar
  9. 9.
    Niezgoda SR, Kalidindi SR: Applications of the phase-coded generalized hough transform to feature detection, analysis, and segmentation of digital microstructures. CMC: Comput Mater Cont 2009, 14(2):79–89.Google Scholar
  10. 10.
    Bunke H, Wang PS: Handbook of character recognition and document image analysis. World Scientific, New Jersey; 1997.Google Scholar
  11. 11.
    Mohri M, Rostamizadeh A, Talwalkar A: Foundations of machine learning. MIT Press, Cambridge, MA, USA; 2012.Google Scholar
  12. 12.
    Junqué de Fortuny E, Martens D, Provost F: Predictive modeling with big data: is bigger really better? J Big Data 2013, 1(4):215–226. 10.1089/big.2013.0037Google Scholar
  13. 13.
    Silver N: The signal and the noise: Why so many predictions fail—but some don't. Penguin Press, New York; 2012.Google Scholar
  14. 14.
    Salem AA, Shaffer JB: Identification and quantification of microtextured regions in materials with ordered crystal structure. 2013.Google Scholar
  15. 15.
    Germain L, Gey N, Humbert M, Bocher P, Jahazi M: Analysis of sharp microtexture heterogeneities in a bimodal IMI 834 billet. Acta Mater 2005, 53(13):3535–3543. 10.1016/j.actamat.2005.03.043Google Scholar
  16. 16.
    Bunge H: Texture analysis in materials science. Butterworths, London; 1982.Google Scholar
  17. 17.
    Adams BL, Kalidindi SR, Fullwood D: Microstructure sensitive design for performance optimization. Butterworth-Heinemann, Newton, MA, USA; 2012.Google Scholar
  18. 18.
    Fullwood DT, Niezgoda SR, Adams BL, Kalidindi SR: Microstructure sensitive design for performance optimization. Prog Mater Sci 2010, 55(6):477–562. 10.1016/j.pmatsci.2009.08.002Google Scholar
  19. 19.
    Houskamp JR, Proust G, Kalidindi SR: Integration of microstructure-sensitive design with finite element methods: elastic-plastic case studies in FCC polycrystals. Int J Multiscale Com 2007, 5(3-4):261–272. 10.1615/IntJMultCompEng.v5.i3-4.80Google Scholar
  20. 20.
    Knezevic M, Kalidindi SR: Fast computation of first-order elastic-plastic closures for polycrystalline cubic-orthorhombic microstructures. Comput Mater Sci 2007, 39(3):643–648. 10.1016/j.commatsci.2006.08.025Google Scholar
  21. 21.
    Proust G, Kalidindi SR: Procedures for construction of anisotropic elastic-plastic property closures for face-centered cubic polycrystals using first-order bounding relations. J Mech Phys Solids 2006, 54(8):1744–1762. 10.1016/j.jmps.2006.01.010Google Scholar
  22. 22.
    Hill R: Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 1963, 11(5):357–372. 10.1016/0022-5096(63)90036-XGoogle Scholar
  23. 23.
    Drugan W, Willis J: A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites. J Mech Phys Solids 1996, 44(4):497–524. 10.1016/0022-5096(96)00007-5Google Scholar
  24. 24.
    Ostoja-Starzewski M: Random field models of heterogeneous materials. Int J Solids Struct 1998, 35(19):2429–2455. 10.1016/S0020-7683(97)00144-3Google Scholar
  25. 25.
    Torquato S: Random heterogeneous materials. Springer-Verlag, New York; 2002.Google Scholar
  26. 26.
    Niezgoda SR, Kanjarla AK, Kalidindi SR: Novel microstructure quantification framework for databasing, visualization, and analysis of microstructure data. Integr Mater Manuf Innov 2013, 2: 3. 10.1186/2193-9772-2-3Google Scholar
  27. 27.
    Niezgoda SR, Yabansu YC, Kalidindi SR: Understanding and visualizing microstructure and microstructure variance as a stochastic process. Acta Mater 2011, 59(16):6387–6400. 10.1016/j.actamat.2011.06.051Google Scholar
  28. 28.
    Niezgoda SR, Turner DM, Fullwood DT, Kalidindi SR: Optimized structure based representative volume element sets reflecting the ensemble-averaged 2-point statistics. Acta Mater 2010, 58(13):4432–4445. 10.1016/j.actamat.2010.04.041Google Scholar
  29. 29.
    Niezgoda SR, Fullwood DT, Kalidindi SR: Delineation of the space of 2-point correlations in a composite material system. Acta Mater 2008, 56(18):5285–5292. 10.1016/j.actamat.2008.07.005Google Scholar
  30. 30.
    Fullwood DT, Niezgoda SR, Kalidindi SR: Microstructure reconstructions from 2-point statistics using phase-recovery algorithms. Acta Mater 2008, 56(5):942–948. 10.1016/j.actamat.2007.10.044Google Scholar
  31. 31.
    Salem AA, Glavicic M, Semiatin S: The effect of preheat temperature and inter-pass reheating on microstructure and texture evolution during hot rolling of Ti-6Al-4-V. Mater Sci Eng A 2008, 496(1):169–176. 10.1016/j.msea.2008.05.017Google Scholar
  32. 32.
    Qidwai SM, Turner DM, Niezgoda SR, Lewis AC, Geltmacher AB, Rowenhorst DJ, Kalidindi SR: Estimating response of polycrystalline materials using sets of weighted statistical volume elements (WSVEs). Acta Mater 2012, 60: 5284–5299. 10.1016/j.actamat.2012.06.026Google Scholar
  33. 33.
    Wargo EA, Hanna AC, Cecen A, Kalidindi SR, Kumbur EC: Selection of representative volume elements for pore-scale analysis of transport in fuel cell materials. J Power Sources 2012, 197: 168–179. 10.1016/j.jpowsour.2011.09.035Google Scholar
  34. 34.
    Torquato S: Inverse optimization techniques for targeted self-assembly. Soft Matter 2009, 5(6):1157–1173. 10.1039/b814211bGoogle Scholar
  35. 35.
    Torquato S: Optimal design of heterogeneous materials. Annu Rev Mater Res 2010, 40: 101–129. 10.1146/annurev-matsci-070909-104517Google Scholar
  36. 36.
    Salem A, Kalidindi SR, Doherty RD: Strain hardening of titanium: role of deformation twinning. Acta Mater 2003, 51(14):4225–4237. 10.1016/S1359-6454(03)00239-8Google Scholar
  37. 37.
    Salem A, Kalidindi S, Semiatin S: Strain hardening due to deformation twinning in α-titanium: constitutive relations and crystal-plasticity modeling. Acta Mater 2005, 53(12):3495–3502. 10.1016/j.actamat.2005.04.014Google Scholar
  38. 38.
    Li H, Mason D, Bieler T, Boehlert C, Crimp M: Methodology for estimating the critical resolved shear stress ratios of α-phase Ti using EBSD-based trace analysis. Acta Mater 2013, 61(20):7555–7567. 10.1016/j.actamat.2013.08.042Google Scholar
  39. 39.
    Kalidindi SR, Bronkhorst CA, Anand L: Crystallographic texture evolution in bulk deformation processing of FCC metals. J Mech Phys Solids 1992, 40(3):537–569. 10.1016/0022-5096(92)80003-9Google Scholar
  40. 40.
    Morris PR, Semiatin SL: The prediction of plastic properties of polycrystalline aggregates of BCC metals deforming by <111 > pencil glide. Texture of Crystalline Solids 1979, 3(2):113–126. 10.1155/TSM.3.113Google Scholar
  41. 41.
    Piehler H, Backofen W: A theoretical examination of the plastic properties of bcc crystals deforming by <111 > pencil glide. Metall Trans 1971, 2(1):249–255. 10.1007/BF02662665Google Scholar
  42. 42.
    Glavicic M, Kobryn P, Goetz R, Yu K, Semiatin S: Texture evolution during primary processing of production-scale vacuum arc remelted ingots of Ti-6Al-4V. In Proc. 10th world conf. on titanium. Wiley-VCH, Weinheim, Germany; 2004:1299–1306.Google Scholar
  43. 43.
    Chin G, Mammel W: Computer solutions of Taylor analysis for axisymmetric flow. Trans Metall Soc AIME 1967, 239(9):1400–1405.Google Scholar
  44. 44.
    Burgers W: On the process of transition of the cubic-body-centered modification into the hexagonal-close-packed modification of zirconium. Physica 1934, 1(7):561–586. 10.1016/S0031-8914(34)80244-3Google Scholar
  45. 45.
    Salem A, Semiatin S: Anisotropy of the hot plastic deformation of Ti-6Al-4-V single-colony samples. Mater Sci Eng A 2009, 508(1):114–120. 10.1016/j.msea.2008.12.035Google Scholar
  46. 46.
    Kröner E: Allgemeine kontinuumstheorie der versetzungen und eigenspannungen. Arch Rational Mech Anal 1959, 4(1):273–334. 10.1007/BF00281393Google Scholar
  47. 47.
    Kalidindi SR: Incorporation of deformation twinning in crystal plasticity models. J Mech Phys Solids 1998, 46(2):267–290. 10.1016/S0022-5096(97)00051-3Google Scholar
  48. 48.
    Glavicic M, Goetz R, Barker D, Shen G, Furrer D, Woodfield A, Semiatin S: Modeling of texture evolution during hot forging of alpha/beta titanium alloys. Metall Mater Trans A 2008, 39(4):887–896. 10.1007/s11661-007-9376-2Google Scholar
  49. 49.
    Lebensohn R, Tomé C: A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: application to zirconium alloys. Acta Metall Mater 1993, 41(9):2611–2624. 10.1016/0956-7151(93)90130-KGoogle Scholar
  50. 50.
    Taylor GI: Plastic strain in metals. J Inst Metals 1938, 62: 307–324.Google Scholar
  51. 51.
    Gey N, Humbert M, Philippe MJ, Combres Y: Investigation of the α- and β- texture evolution of hot rolled Ti-64 products. Mater Sci Eng A 1996, 219(1-2):80–88. 10.1016/S0921-5093(96)10388-9Google Scholar
  52. 52.
    Wu X, Kalidindi SR, Necker C, Salem AA: Prediction of crystallographic texture evolution and anisotropic stress–strain curves during large plastic strains in high purity α-titanium using a Taylor-type crystal plasticity model. Acta Mater 2007, 55(2):423–432. 10.1016/j.actamat.2006.08.034Google Scholar
  53. 53.
    Kalidindi SR, Duvvuru HK, Knezevic M: Spectral calibration of crystal plasticity models. Acta Mater 2006, 54(7):1795–1804. 10.1016/j.actamat.2005.12.018Google Scholar
  54. 54.
    Lebensohn RA, Rollett AD, Suquet P: Fast Fourier transform-based modeling for the determination of micromechanical fields in polycrystals. JOM 2011, 63(3):13–18. 10.1007/s11837-011-0037-yGoogle Scholar
  55. 55.
    Knezevic M, Al-Harbi HF, Kalidindi SR: Crystal plasticity simulations using discrete Fourier transforms. Acta Mater 2009, 57(6):1777–1784. 10.1016/j.actamat.2008.12.017Google Scholar
  56. 56.
    Al-Harbi HF, Knezevic M, Kalidindi SR: Spectral approaches for the fast computation of yield surfaces and first-order plastic property closures for polycrystalline materials with cubic-triclinic textures. CMC: Comput Mater Cont 2010, 15(2):153–172.Google Scholar
  57. 57.
    6.13. Dassault Systémes, Providence, RI, USA; 2014.Google Scholar
  58. 58.
    2013.1. MSC Software, Newport Beach, CA, USA; 2013.Google Scholar
  59. 59.
    Simufact.forming (2014) Simufact engineering GmbH. Hamburg, Germany Simufact.forming (2014) Simufact engineering GmbH. Hamburg, GermanyGoogle Scholar
  60. 60.
    Al-Harbi HF, Kalidindi SR (2014) Crystal plasticity finite element simulations using a database of discrete Fourier transforms. Int J Plast doi:10.1016/j.ijplas.2014.04.006 Al-Harbi HF, Kalidindi SR (2014) Crystal plasticity finite element simulations using a database of discrete Fourier transforms. Int J Plast doi:10.1016/j.ijplas.2014.04.006Google Scholar
  61. 61.
    Al-Harbi HF, Landi G, Kalidindi SR: Multi-scale modeling of the elastic response of a structural component made from a composite material using the materials knowledge system. Modell Simul Mater Sci Eng 2012, 20: 055001. 10.1088/0965-0393/20/5/055001Google Scholar
  62. 62.
    Fast T, Niezgoda SR, Kalidindi SR: A new framework for computationally efficient structure–structure evolution linkages to facilitate high-fidelity scale bridging in multi-scale materials models. Acta Mater 2011, 59(2):699–707. 10.1016/j.actamat.2010.10.008Google Scholar
  63. 63.
    Kalidindi SR, Niezgoda SR, Landi G, Vachhani S, Fast T: A novel framework for building materials knowledge systems. CMC: Comput Mater Cont 2010, 17(2):103–125.Google Scholar
  64. 64.
    Landi G, Niezgoda SR, Kalidindi SR: Multi-scale modeling of elastic response of three-dimensional voxel-based microstructure datasets using novel DFT-based knowledge systems. Acta Mater 2010, 58(7):2716–2725. 10.1016/j.actamat.2010.01.007Google Scholar
  65. 65.
    Landi G, Kalidindi SR: Thermo-elastic localization relationships for multi-phase composites. CMC: Comput Mater Cont 2010, 16(3):273–293.Google Scholar
  66. 66.
    Adams BL, Kalidindi SR, Fullwood DT: Microstructure sensitive design for performance optimization. Science, Elsevier; 2012.Google Scholar
  67. 67.
    Kroner E: Statistical modelling. In Modelling small deformations of polycrystals. Edited by: Gittus J, Zarka J. Elsevier Science Publishers, London; 1986:229–291. 10.1007/978-94-009-4181-6_8Google Scholar
  68. 68.
    Kroner E: Bounds for effective elastic moduli of disordered materials. J Mech Phys Solids 1977, 25(2):137–155. 10.1016/0022-5096(77)90009-6Google Scholar
  69. 69.
    Binci M, Fullwood D, Kalidindi SR: A new spectral framework for establishing localization relationships for elastic behavior of composites and their calibration to finite-element models. Acta Mater 2008, 56(10):2272–2282. 10.1016/j.actamat.2008.01.017Google Scholar
  70. 70.
    Kalidindi SR, Binci M, Fullwood D, Adams BL: Elastic properties closures using second-order homogenization theories: case studies in composites of two isotropic constituents. Acta Mater 2006, 54(11):3117–3126. 10.1016/j.actamat.2006.03.005Google Scholar
  71. 71.
    Fast T, Kalidindi SR: Formulation and calibration of higher-order elastic localization relationships using the MKS approach. Acta Mater 2011, 59(11):4595–4605. 10.1016/j.actamat.2011.04.005Google Scholar
  72. 72.
    Kalidindi SR (2012) Computationally-efficient fully-coupled multi-scale modeling of materials phenomena using calibrated localization linkages. ISRN Materials Science doi:10.5402/2012/305692 Kalidindi SR (2012) Computationally-efficient fully-coupled multi-scale modeling of materials phenomena using calibrated localization linkages. ISRN Materials Science doi:10.5402/2012/305692Google Scholar
  73. 73.
    Kalidindi S, Anand L: An approximate procedure for predicting the evolution of crystallographic texture in bulk deformation processing of FCC metals. Int J Mech Sci 1992, 34(4):309–329. 10.1016/0020-7403(92)90038-IGoogle Scholar
  74. 74.
    Kraska M, Doig M, Tikhomirov D, Raabe D, Roters F: Virtual material testing for stamping simulations based on polycrystal plasticity. Comput Mater Sci 2009, 46(2):383–392. 10.1016/j.commatsci.2009.03.025Google Scholar

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© Salem et al.; licensee Springer. 2014

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Authors and Affiliations

  • Ayman A Salem
    • 1
    Email author
  • Joshua B Shaffer
    • 1
  • Daniel P Satko
    • 1
  • S Lee Semiatin
    • 2
  • Surya R Kalidindi
    • 3
  1. 1.Materials Resources LLCDaytonUSA
  2. 2.Materials and Manufacturing DirectorateAir Force Research LaboratoryWright-PattersonUSA
  3. 3.Georgia Institute of TechnologyAtlantaUSA

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